The purpose of this note is to explore further possible experimental tests for the non-linear lattice dynamics explanation [1]}, [2]}, [3]} of light-enhanced superconductivity in \(YBa_{2}Cu_{3}O_{6+x}\)  [4]}, [5]}, [6]}. According to this explanation, one (or more) optical phonon \(A_{1g}\) -symmetric mode coordinate, \(Q\) , is pushed off its equilibrium value by excitation of an infrared-active mode \(Q_{IR}\) , due to a nonlinear coupling that, according to Mankowsky's et al. arguments is of the form \( -a_{1,2} Q Q_{IR}^{2}\) . Indeed, when this term is added to the harmonic potentials and the kinetic energies of the \( Q_{IR}, Q\)  oscillators, the Barbanis Hamiltonian [7]} is obtained, which has been first investigated in the context of celestial mechanics, then in studies of quantum ergodicity and molecular physics [8]},[9]}, [10]}; and it turns out that an accurate approximation to the exact eigenfunctions of this Hamiltonian is given by eigenfunctions of the form [9]}, [10]}:
\(\Phi _{n_1,n_2} = N\phi _{n_1}(aQ+b) \phi _{n_2}(a_{IR}Q_{IR})\) 
